1/2x+1/4y=6. 1/5x+1/3y=1

Answers

Answer 1

Answer: $(1)/(2)x+(1)/(4)y=6 \ \ \ |* 2 \n(1)/(5)x+(1)/(3)y=1 \ \ \ |* (-5) \n \nx+(1)/(2)y=12 \n\underline{-x-(5)/(3)y=-5} \n(1)/(2)y-(5)/(3)y=12-5 \n(3)/(6)y-(10)/(6)y=7 \n-(7)/(6)y=7 \ny=7 * (-(6)/(7)) \ny=-6 \n \nx+(1)/(2)y=12 \nx+(1)/(2) * (-6)=12 \nx-3=12 \nx=12+3 \nx=15 \n \n\boxed{(x,y)=(15,-6)}$

Answer 2

Answer: 1st Step:

$\frac { 1 }{ 2 } x+\frac { 1 }{ 4 } y=6\n \n 4\left( \frac { 1 }{ 2 } x+\frac { 1 }{ 4 } y \right) =6\cdot 4\n \n 2x+y=24\n \n y=24-2x$

2nd Step:

$\frac { 1 }{ 5 } x+\frac { 1 }{ 3 } y=1\n \n 15\left( \frac { 1 }{ 5 } x+\frac { 1 }{ 3 } y \right) =1\cdot 15$

$\n \n 3x+5y=15\n \n 5y=15-3x\n \n 5y=3\left( 5-x \right) \n \n y=\frac { 3\left( 5-x \right) }{ 5 }$

3rd Step:

$\frac { 3\left( 5-x \right) }{ 5 } =24-2x$

$\n \n 5\cdot \frac { 3\left( 5-x \right) }{ 5 } =5\left( 24-2x \right) \n \n 3\left( 5-x \right) =120-10x$

$\n \n 15-3x=120-10x\n \n -3x+10x=120-15\n \n 7x=105\n \n x=\frac { 105 }{ 7 }$

$\n \n \therefore \quad x=15$

4th Step (When x=15):

$y=24-2\left( 15 \right) \n \n y=24-30\n \n \therefore \quad y=-6$

x + 2y = 2

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=(y_2-y_1)/(x_2-x_1)$

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We have the points (-6, 4) and (2, 0).

Substitute:

$m=(0-4)/(2-(-6))=(-4)/(8)=-(1)/(2)$

Put the value of the slope and coordinates of the point (2, 0) to the equation of a line:

$0=-(1)/(2)(2)+b$

$0=-1+b$ add 1 to both sides

$1=b\to b=1$

The equation of a line in the slope-intercept form:

$y=-(1)/(2)x+1$

Convert to the standard form $Ax+By=C$

$y=-(1)/(2)x+1$ multiply both sides by 2

$2y=-x+2$ add x to both sides

$x+2y=2$

Answer:

Option 1.

Step-by-step explanation:

It is given that the line passes through the points (-6,4) and (2,0).

If a line passes through two points, then the equation of line is

$y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)$

Using the above formula the equation of line is

$y-(4)=(0-4)/(2-(-6))(x-(-6))$

$y-4=(-4)/(8)(x+6)$

$y-4=(-1)/(2)(x+6)$

Muliply both sides by 2.

$2y-8=-x-6$

$x+2y=-6+8$

$x+2y=2$

Therefore, the correct option is 1.

Find the percent of increase:
Year 2005 2010
Population 3.2

(millions) 5.6

Answers

Answer:

the answer is x4sqaured=2

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Step-by-step explanation:

A meteorite found in United States weighs 7/10 as much as one found in Mongolia. The meteorite found in Mongolia weighs 22 tons. How much does the meteorite found in United States weigh?

Answers

Answer: The meteorite found in United States weigh 15.4 tons.

Step-by-step explanation:

Since we have given that

Weight of Mongolia meteorite = 22 tons

According to question, we get that

A meteorite found in United States weighs 7/10 as much as one found in Mongolia

So, Weight of meteorite in United states would be

$(7)/(10)* 22\n\n=0.7* 22\n\n=15.4\ tons$

Hence, the meteorite found in United States weigh 15.4 tons.

15.4 tons is the weigh of the meteorite

6 more than the difference of b and 5

Answers

The answer would be b-5+6

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 40 books. A total of 13 boxes were sent which can hold 360 books altogether. Graphically solve a system of equations in order to determine the number of small boxes sent, x,x, and the number of large boxes sent, yy.Click twice to plot each line. Click a line to delete it.

Answers

Answer:

The Answer is: There are 5 large boxes and 8 small boxes. (The graphical plot will need to be solved using the software).

Step-by-step explanation:

Let xx = small boxes and yy = large boxes:

xx + yy = 13

xx = 13 - yy

The number of small boxes times 20, plus the number of large boxes times 40 is equal to 360:

20xx + 40yy = 360

Substitute the algebraic value of xx, so we only have one variable to consider and solve for yy:

20(13 - yy) + 40yy = 360

260 - 20yy + 40yy = 360

260 + 20yy = 360

20yy = 100

yy = 100 / 20 = 5 large boxes.

Solve for xx:

xx = 13 - yy

xx = 13 - 5 = 8 small boxes.

There are 5 large boxes and 8 small boxes. (The graphical plot will need to be solved using the software).

Proof:

20xx + 40yy = 360

20(8) + 40(5) = 360

160 + 200 = 360

360 = 360

Final answer:

To solve the problem graphically, set up a system of equations: x + y = 13 and 20x + 40y = 360. Graph the equations to find the intersection point which represents the solution.

Explanation:

To solve this problem graphically, we can set up a system of equations based on the given information. Let's denote the number of small boxes as x and the number of large boxes as y. From the given information, we can write the following equations:

x + y = 13 (equation 1, representing the total number of boxes)

20x + 40y = 360 (equation 2, representing the total number of books)

To graph these equations, we can plot them on a coordinate plane, where the x-axis represents the number of small boxes (x) and the y-axis represents the number of large boxes (y). The intersection point of these two lines will represent the solution to the system of equations, giving us the values of x and y (the number of small and large boxes sent, respectively).